Multilinear Algebra

Multilinearity of the determinant
In this video, I define the notion of a multilinear function and I show that the determinant is multilinear. Come and get a taste of the beauty of multilinear algebra :)
Check out my Determinants Playlist: • Determinants
Subscribe to my channel: / drpeyam

[@TheNachoesuncapo]

The fact that a professional researcher mathematician is uploading this videos for free is something we should all be so grateful of

[@Centurion256]

I like how in math there's always a way to go beyond. No matter which concept you choose, there's always some way you can expand on it.
Like REAL numbers? Might as well take a look at (un)real(Imaginary) numbers! Like both? Here you go: complex numbers! What's that? Not enough dimensions? Too many properties?(Still commutative and associative), Well here are the hyper-complex numbers(quaternions, octonions, sedenions)! And the list goes on and on...
And that's true for any other concept in math, It's always fascinating to grasp more and more abstract structures. Perhaps there is no end to it...

[@drpeyam]

Yeah, in math you never get bored :)

[@thedoublehelix5661]

I also love the abstractions of math. Going from simple computations to variables in algebra to functions in calculus to vector spaces in linear algebra is fascinating. Also many problems in math can be solved by thinking more abstractly. Talking about abstract vectors and matrices when solving systems of equations or finding the inflaction point to find the cubic formula or doing algebraic manipulations to simplify a large computation.

[@WinnerMin17]

Minecraft

[@Songvbm]

I was lucky to discover his channel and I enjoy everything he teaches

[@TheRealSlimPiggy]

Your enthusiams inspire me

[@maxisjaisi400]

It would be nice if you could talk about general tensor product of vector spaces

[@jamelbenahmed4788]

Amazing

[@JaydentheMathGuy]

Me(just a senior in A.P. Calc B.C. and A.P. Physics1&2)Multilinear Algebra??? QUADRATIC ALGEBRA !
*watches this video*
me:...

[@theproofessayist8441]

Complex Number Algebra, Quaternion Algebra, Octonion Algebra, Sedonion Algebra!!!!! - making your life painful BUT INTERESTING by limiting the rules/properties you could use from your everyday real number field one at a time.

[@tracyh5751]

not only is the determinant multilinear, it is alternating as well. :)

[@drpeyam]

Yeah! There will be more on them :)

[@Songvbm]

Is multilinear algebra all about the linear transformations and determinants!!!

[@HakanTheUltimateHoca]

5:06 oh :(